Composition operators acting on holomorphic Sobolev spaces

被引：11

作者：

Choe, BR ^{[1
]}

Koo, H

Smith, W

机构：

[1] Korea Univ, Dept Math, Seoul 136701, South Korea

[2] Univ Hawaii, Dept Math, Honolulu, HI 96822 USA

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2003年 / 355卷 / 07期

关键词：

composition operator; fractional derivative; Bergman space;

D O I：

10.1090/S0002-9947-03-03273-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the action of composition operators on Sobolev spaces of analytic functions having fractional derivatives in some weighted Bergman space or Hardy space on the unit disk. Criteria for when such operators are bounded or compact are given. In particular, we find the precise range of orders of fractional derivatives for which all composition operators are bounded on such spaces. Sharp results about boundedness and compactness of a composition operator are also given when the inducing map is polygonal.

引用

页码：2829 / 2855

页数：27

共 19 条

[1]

[Anonymous], 1989, DISSERTATIONES MATH

[2]

COWEN C., 1995, Studies in Advanced Mathematics

[3]

Duren P. L., 1970, PURE APPL MATH, V38, DOI [10.1016/S0079-8169(08)62672-0, DOI 10.1016/S0079-8169(08)62672-0]

[4]

Garnett J. B., 1981, PURE APPL MATH, V96